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Simplifying 9x2 + 13x + -32 = 0 Reorder the terms: -32 + 13x + 9x2 = 0 Solving -32 + 13x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.555555556 + 1.444444444x + x2 = 0 Move the constant term to the right: Add '3.555555556' to each side of the equation. -3.555555556 + 1.444444444x + 3.555555556 + x2 = 0 + 3.555555556 Reorder the terms: -3.555555556 + 3.555555556 + 1.444444444x + x2 = 0 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + 1.444444444x + x2 = 0 + 3.555555556 1.444444444x + x2 = 0 + 3.555555556 Combine like terms: 0 + 3.555555556 = 3.555555556 1.444444444x + x2 = 3.555555556 The x term is 1.444444444x. Take half its coefficient (0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. 1.444444444x + 0.5216049380 + x2 = 3.555555556 + 0.5216049380 Reorder the terms: 0.5216049380 + 1.444444444x + x2 = 3.555555556 + 0.5216049380 Combine like terms: 3.555555556 + 0.5216049380 = 4.077160494 0.5216049380 + 1.444444444x + x2 = 4.077160494 Factor a perfect square on the left side: (x + 0.722222222)(x + 0.722222222) = 4.077160494 Calculate the square root of the right side: 2.019197983 Break this problem into two subproblems by setting (x + 0.722222222) equal to 2.019197983 and -2.019197983.Subproblem 1
x + 0.722222222 = 2.019197983 Simplifying x + 0.722222222 = 2.019197983 Reorder the terms: 0.722222222 + x = 2.019197983 Solving 0.722222222 + x = 2.019197983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = 2.019197983 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = 2.019197983 + -0.722222222 x = 2.019197983 + -0.722222222 Combine like terms: 2.019197983 + -0.722222222 = 1.296975761 x = 1.296975761 Simplifying x = 1.296975761Subproblem 2
x + 0.722222222 = -2.019197983 Simplifying x + 0.722222222 = -2.019197983 Reorder the terms: 0.722222222 + x = -2.019197983 Solving 0.722222222 + x = -2.019197983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = -2.019197983 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = -2.019197983 + -0.722222222 x = -2.019197983 + -0.722222222 Combine like terms: -2.019197983 + -0.722222222 = -2.741420205 x = -2.741420205 Simplifying x = -2.741420205Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.296975761, -2.741420205}
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